{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "# Sequential Quadratic Programming"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "(which is just using Newton on a Lagrangian)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import numpy.linalg as la"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Here's an objective function $f$ and a constraint $g(x)=0$:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "def f(vec):\n",
        "    x = vec[0]\n",
        "    y = vec[1]\n",
        "    return (x-2)**4 + 2*(y-1)**2\n",
        "\n",
        "def g(vec):\n",
        "    x = vec[0]\n",
        "    y = vec[1]\n",
        "    return x + 4*y - 3"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Now define the Lagrangian, its gradient, and its Hessian:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "\n",
        "def L(vec):\n",
        "    lam = vec[2]\n",
        "    return f(vec) + lam * g(vec)\n",
        "\n",
        "def grad_L(vec):\n",
        "    x = vec[0]\n",
        "    y = vec[1]\n",
        "    lam = vec[2]\n",
        "    \n",
        "    return np.array([\n",
        "        4*(x-2)**3 + lam,\n",
        "        4*(y-1) + 4*lam,\n",
        "        x+4*y-3\n",
        "        ])\n",
        "\n",
        "def hess_L(vec):\n",
        "    x = vec[0]\n",
        "    y = vec[1]\n",
        "    lam = vec[2]\n",
        "    \n",
        "    return np.array([\n",
        "        [12*(x-2)**2, 0, 1],\n",
        "        [0, 4, 4],\n",
        "        [1, 4, 0]\n",
        "        ])    "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "At this point, we only need to find an *unconstrained* minimum of the Lagrangian!\n",
        "\n",
        "Let's fix a starting vector `vec`:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "vec = np.zeros(3)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Implement Newton and run this cell in place a number of times (Ctrl-Enter):"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 18,
      "metadata": {
        "collapsed": false
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([ 1.46398989,  0.38400253,  0.61599747])"
            ]
          },
          "execution_count": 18,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "vec = vec - la.solve(hess_L(vec), grad_L(vec))\n",
        "vec"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Let's first check that we satisfy the constraint:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 21,
      "metadata": {
        "collapsed": false
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "0.0"
            ]
          },
          "execution_count": 21,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "g(vec)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Next, let's look at a plot:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 22,
      "metadata": {
        "collapsed": false
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7fd6b4398390>]"
            ]
          },
          "execution_count": 22,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": 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Ws46VlNJCM+MYz/5M7FVr7odAUE0HK6ljE81spYVOPAzTKuIwMhlKBpm/YrSL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\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7fd6b43baf28>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "import matplotlib.pyplot as pt\n",
        "x, y = np.mgrid[0:4:30j, -3:5:30j]\n",
        "pt.contour(x, y, f(np.array([x,y])), 20)\n",
        "pt.contour(x, y, g(np.array([x,y])), levels=[0])\n",
        "pt.plot(vec[0], vec[1], \"o\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": []
    }
  ],
  "metadata": {},
  "nbformat": 4,
  "nbformat_minor": 0
}